The present invention relates to a method for the automated joining of two-dimensional objects such as images, maps or images cropped from them.
Even in the context of digital image processing, the joining of images and cropped images as in photo montage is still done essentially by hand. In such a method, for example, a retoucher, selects a cropped segment from a first image which is to be incorporated in a second image at a given point, while possibly using an image processing computer to perform simple operations of distortion, enlargement or reduction in order to incorporate the selected cropped image as seamlessly as possible into the second image. The quality of the transition depends to a great extent on the skill and patience of the retoucher.
A method for the automated joining of two-dimensional objects is proposed which can be applied rapidly and reproducibly even by inexperienced persons and which opens up applications for the automated joining of objects extending far beyond photo montage.
The method includes selecting a first and a second set of points of the first and the second object, respectively, one point of the second set being assigned precisely to each point of the first set, and vice versa, then solving an equation system completely automatically which can be obtained by setting up a transformation equation T for the points of the first set with variable transformation parameters a and by determining those values of parameters a for which the sum of all the points of the squared values of the distances between a point T (Pi) obtained by transformation of a point of the first set and a point Gi of the second set assumes a minimum, and finally plotting the first object onto the second one with the aid of transformation equation T thus obtained. While the points of the two sets are advantageously selected by a user, the subsequent calculation of the transformation equation and the plotting are well suited to being accomplished fully automatically by a computer or the like. The computational technique of the method can be kept particularly simple if each point is represented by a complex number.
Conventional methods of analysis can be used to determine the values sought for parameters a.
A preferred special case of the method according to the present invention is a method for the automated joining of two-dimensional objects in which transformation function T has the form of a polynomial. In this case, the values of parameters a, for which the sum of the squared distances between the transformed points of the first set and the assigned points of the second set assumes a minimum, are given by equation system 1.                               (                                                                                          ∑                    i                                    ⁢                                                            G                      i                                        ⁢                                          P                      i                                              n                        *                                                                                                                                                ⋮                                                                                                          ∑                    i                                    ⁢                                                            G                      i                                        ⁢                                          P                      i                      *                                                                                                                                                                ∑                    i                                    ⁢                                      G                    i                                                                                )                =                              (                                                                                                      ∑                      i                                        ⁢                                                                  P                        i                        n                                            ⁢                                              P                        i                                                  n                          *                                                                                                                                      ⋯                                                                                            ∑                      i                                        ⁢                                                                  P                        i                                            ⁢                                              P                        i                                                  n                          *                                                                                                                                                                                ∑                      i                                        ⁢                                          P                      i                                              n                        *                                                                                                                                          ⋮                                                                      xe2x80x83                                                                    ⋮                                                  ⋮                                                                                                                        ∑                      i                                        ⁢                                                                  P                        i                        n                                            ⁢                                              P                        i                        *                                                                                                              ⋯                                                                                            ∑                      i                                        ⁢                                                                  P                        i                                            ⁢                                              P                        i                        *                                                                                                                                                        ∑                      i                                        ⁢                                          P                      i                      *                                                                                                                                                              ∑                      i                                        ⁢                                          P                      i                      n                                                                                        ⋯                                                                                            ∑                      i                                        ⁢                                          P                      i                                                                                                                                  ∑                      i                                        ⁢                    1                                                                        )                    ⁢                      (                                                                                a                    n                                                                                                ⋮                                                                                                  a                    1                                                                                                                    a                    0                                                                        )                                              (        1        )            
The solution of such linear equation systems poses no difficulties of any kind and can be accomplished fully automatically with an appropriately programmed computer or microprocessor.
If the number of free parameters a is equal to the number m of points of the first set, then a transformation T is obtained, which plots each point Pi, i=1, . . . , m of the first set precisely onto the corresponding point Gi of the second set. Thus, in the case of a photo montage, there is no difficulty at all in causing any number of transitions of contours or lines that intersect the boundary lines of joined images to merge continuously, a user first selecting end points of these lines or contours that are intended to match and to coincide at each of the edges of the two images, the transformation equation then being calculated by a computer. Thus, the boundary line can be made to be extremely inconspicuous and the montage practically unrecognizable as such.
In a preferred application of the method, each of the objects is a map stored on a data medium and the joined objects are displayed on a screen. Such a method is suitable for use in a vehicle navigation system in particular.